"When students can connect mathematical ideas, their understanding is deeper and more lasting. They can see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experience. Through instruction that emphasizes the interrelatedness of mathematical ideas, students not only learn mathematics, they also learn about the utility of mathematics."

(NCTM, 2000, p. 64)

As we look at the Connections Standard, we will consider several aspects of connections in mathematical learning and teaching. We want students to recognize that mathematical ideas connect and build on one another. Additionally, connecting mathematics to other subject areas as well as to applications in the world outside the classroom is equally important. Mathematics instruction that focuses on the relationships between concepts helps students develop a deeper understanding of those concepts.

We will begin with an introduction to a two-dimensional shape called a hexomino, and then present two examples of upper elementary student work for you to consider. As you observe these problems, think about the range of possible connections: among mathematical topics, to the process standards, and beyond mathematics.